MEN OF MATHEMATICS line drawn through the fixed point and lying within the angle formed by the two parallels. This apparently bizarre situation is 'realized' by the geodesies on a pseudosphere. For any everyday purpose (measurements of distances, etc.), the differences between the geometries of Euclid and Lobat- chewsky are too small to count, but this is not the point of importance: each is self-consistent and each is adequate for human experience. Lobatchewsky abolished the necessary *truth' of Euclidean geometry. His geometry was but the first of several constructed by his successors. Some of these substi- tutes for Euclid's geometry - for instance the Riemannian geometry of general relativity - are to-day at least as important in the still living and growing parts of physical science as Euclid's wass and is, in the comparatively static and classical parts. For some purposes Euclid's geometry is best or at least sufficient, for others it is inadequate and a non-Euclidean geometry is demanded. Euclid in some sense was believed for 2,200 years to have discovered an absolute truth or a necessary mode of human perception in his system of geometry. Lobatchewsky's creation was a pragmatic demonstration of the error of this belief. The boldness of his challenge and its successful outcome have inspired mathematicians and scientists in general to challenge other 'axioms' or accepted truths', for example the 'law* of causalityr which, for centuries, have seemed as necessary to straight thinking as Euclid's postulate appeared till Lobat- chewsky discarded it, The full impact of the LobatchewsMan method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobatchewsky the Copernicus of Geometry, for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.